src/math/generic/sincosf_utils.h

//===-- Collection of utils for sinf/cosf/sincosf ---------------*- C++ -*-===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//

#ifndef LLVM_LIBC_SRC_MATH_SINCOSF_UTILS_H
#define LLVM_LIBC_SRC_MATH_SINCOSF_UTILS_H

#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/FPUtil/PolyEval.h"
#include "src/__support/common.h"

#if defined(LIBC_TARGET_HAS_FMA)
#include "range_reduction_fma.h"
// using namespace __llvm_libc::fma;
using __llvm_libc::fma::FAST_PASS_BOUND;
using __llvm_libc::fma::large_range_reduction;
using __llvm_libc::fma::small_range_reduction;
#else
#include "range_reduction.h"
// using namespace __llvm_libc::generic;
using __llvm_libc::generic::FAST_PASS_BOUND;
using __llvm_libc::generic::large_range_reduction;
using __llvm_libc::generic::small_range_reduction;
#endif // LIBC_TARGET_HAS_FMA

namespace __llvm_libc {

// Lookup table for sin(k * pi / 16) with k = 0, ..., 31.
// Table is generated with Sollya as follow:
// > display = hexadecimal;
// > for k from 0 to 31 do { D(sin(k * pi/16)); };
const double SIN_K_PI_OVER_16[32] = {
    0x0.0000000000000p+0,  0x1.8f8b83c69a60bp-3,  0x1.87de2a6aea963p-2,
    0x1.1c73b39ae68c8p-1,  0x1.6a09e667f3bcdp-1,  0x1.a9b66290ea1a3p-1,
    0x1.d906bcf328d46p-1,  0x1.f6297cff75cb0p-1,  0x1.0000000000000p+0,
    0x1.f6297cff75cb0p-1,  0x1.d906bcf328d46p-1,  0x1.a9b66290ea1a3p-1,
    0x1.6a09e667f3bcdp-1,  0x1.1c73b39ae68c8p-1,  0x1.87de2a6aea963p-2,
    0x1.8f8b83c69a60bp-3,  0x0.0000000000000p+0,  -0x1.8f8b83c69a60bp-3,
    -0x1.87de2a6aea963p-2, -0x1.1c73b39ae68c8p-1, -0x1.6a09e667f3bcdp-1,
    -0x1.a9b66290ea1a3p-1, -0x1.d906bcf328d46p-1, -0x1.f6297cff75cb0p-1,
    -0x1.0000000000000p+0, -0x1.f6297cff75cb0p-1, -0x1.d906bcf328d46p-1,
    -0x1.a9b66290ea1a3p-1, -0x1.6a09e667f3bcdp-1, -0x1.1c73b39ae68c8p-1,
    -0x1.87de2a6aea963p-2, -0x1.8f8b83c69a60bp-3};

static inline void sincosf_eval(double xd, uint32_t x_abs, double &sin_k,
                                double &cos_k, double &sin_y, double &cosm1_y) {
  int64_t k;
  double y;

  if (likely(x_abs < FAST_PASS_BOUND)) {
    k = small_range_reduction(xd, y);
  } else {
    fputil::FPBits<float> x_bits(x_abs);
    k = large_range_reduction(xd, x_bits.get_exponent(), y);
  }

  // After range reduction, k = round(x * 16 / pi) and y = (x * 16 / pi) - k.
  // So k is an integer and -0.5 <= y <= 0.5.
  // Then sin(x) = sin((k + y)*pi/16)
  //             = sin(y*pi/16) * cos(k*pi/16) + cos(y*pi/16) * sin(k*pi/16)

  sin_k = SIN_K_PI_OVER_16[k & 31];
  // cos(k * pi/16) = sin(k * pi/16 + pi/2) = sin((k + 8) * pi/16).
  // cos_k = y * cos(k * pi/16)
  cos_k = SIN_K_PI_OVER_16[(k + 8) & 31];

  double ysq = y * y;

  // Degree-6 minimax even polynomial for sin(y*pi/16)/y generated by Sollya
  // with:
  // > Q = fpminimax(sin(y*pi/16)/y, [|0, 2, 4, 6|], [|D...|], [0, 0.5]);
  sin_y = y * fputil::polyeval(ysq, 0x1.921fb54442d17p-3, -0x1.4abbce6256adp-10,
                               0x1.466bc5a5ac6b3p-19, -0x1.32bdcb4207562p-29);
  // Degree-8 minimax even polynomial for cos(y*pi/16) generated by Sollya with:
  // > P = fpminimax(cos(x*pi/16), [|0, 2, 4, 6, 8|], [|1, D...|], [0, 0.5]);
  // Note that cosm1_y = cos(y*pi/16) - 1.
  cosm1_y =
      ysq * fputil::polyeval(ysq, -0x1.3bd3cc9be45dcp-6, 0x1.03c1f081b08ap-14,
                             -0x1.55d3c6fb0fb6ep-24, 0x1.e1d3d60f58873p-35);
}

} // namespace __llvm_libc

#endif // LLVM_LIBC_SRC_MATH_SINCOSF_UTILS_H